This invention relates to a means of pressurizing hot flue gases so that the gases can be moved through a heat recovery device and more specifically, to a reactive impeller for pressurizing hot flue gas.
In many energy-intensive, high-temperature industrial processes operating in a range of temperature from about 2000.degree. Farenheit (F.) to 3800.degree. F., products of combustion are rejected as flue gases. These gases frequently have a temperature of about 2000.degree.-2200.degree. F. or more. As a result, flue gases frequently carry off more than half the heating value of the combustion reactants. As an example, flue gas (fg) discarded at 2000.degree. F. from the combustion of methane in air (a) without air preheat carries off 57.3% of the gross heating value of the fuel. Only the fraction f.sub.a of the gross heating value of the fuel has done useful heating, where: ##EQU1## x is the excess air fraction, as for instance, in CH.sub.4 +(1+x)2(O.sub.2 +3.76 N.sub.2)=CO.sub.2 +2H.sub.2 O+2xO.sub.2 +(1+x)7.52 N.sub.2. Operating at 110% theoretical air, without preheat, x=0.1, r.sub.a =17.16(1+x)=18.876, r.sub.fg =19.876, hhv=23,875 Btu/lb, and ##EQU2##
Therefore, 100%(1-0.386)=61.4% of the gross heating value of the flue is lost.
Recovery of this residual energy is obviously desirable. The thermodynamically most efficient way to recover the energy is by preheating the combustion reactants. For instance, preheating the 110% theoretical air to 1400.degree. F. results in adding to the previously computed value of f.sub.a the term ##EQU3## or 18.876(340)/23,876=0.269. EQU f.sub.a =0.9-0.514+0.269=0.655
In this way, 65.5% of the hhv of the fuel is available to the process and only 34.5% is lost. A most effective preheating device is a continuously-operating recuperator. However, in many processes, such as the combustion process in direct-fired industrial furnaces, the gases have a near-zero static pressure. As a result, no pressure potential exists for moving the gas through the recuperator. Conventional solutions for the problem thus presented are chimneys and eductors, i.e., jet pumps. These ordinary means of moving hot gases are grossly inefficient. For example, the thermal efficiency of a chimney is generally a fraction of one percent. An unconventional solution would be a fan or blower, as commonly used for low temperature gases. Such a device would permit the use of a continuous heat recuperator and thereby surpass the thermal efficiency of the chimney by a ratio of about 100 to 1.
For a fair comparison of the chimney, eductor and fan, the power produced by each device, i.e., the generated pressure rise .DELTA.P multipled by the volume flow rate V, .DELTA.pV, is divided by the rate at which thermal energy is supplied to the system before it is upgraded to shaft power or the power of the entraining jet. An elementary calculation for each device is as follows.
The Chimney Of Height H: PA1 For T.sub.air =537.degree. R, c.sub.p,fg =0.26, .eta. (in %)=H/1000. PA1 The Jet Pump: PA1 The Fan:
Driven by the buoyant force due to the temperature excess .DELTA.t of the flue gas over the ambient air, the efficiency .eta. is as follows: ##EQU4## where c.sub.p is specific heat at constant pressure, Btu/lbm .degree.F.; g.sub.c is a conversion factor 32.2 (lbm) (f)/lbf/sec.sup.2, .rho. is density, lbm/ft.sup.3 ; and T is absolute temperature.
This means that a 400-ft stack is only 0.4% efficient as a "mover" of gas.
A modern annular jet pump may have an efficiency of up to 50%, although efficiencies of 20-40% are much more likely. Assuming that the driving stream is powered by an 80%-efficient compressor driven by a 35%-efficient electric motor, .eta.=(0.4)(0.8)(0.35)100%=11%.
A well-designed axial-flow fan or blower can approach 80% air-power-to-shaft-power efficiency. Allowing for 35% efficiency in generating electricity, .eta.=0.8(0.35) 100%=28%.
Roughly, then, the energy efficiencies of the three different means of pressurizing, or imparting momentum to, a hot stream of flue gas are in the ratio 1 to 30 to 100 (stack to jet pump to fan). A mechanically driven fan is clearly superior, were it not for the high temperatures involved. However, while energy efficient, the fan or blower would have its blades present in the flue gases, at blade temperature of 2000.degree. F. or more. Since even advanced and exotic turbine-blade alloys soften, flow and melt above 1750.degree.-1800.degree. F., the common fan could not withstand the heat of 2000.degree. F. flue gases even if refined with exotic-blade alloys.
To explain, iron softens or melts at 2822.degree. F., nickel at 2677.degree. F., and while most nickel-based alloys melt between 2190.degree. and 2370.degree. F., their tensile (rupture) strength deteriorates rapidly above 1500.degree. F. Strength curves of Incoloy 901 (0.04% C, 13 Cr, 3 Ti, 2 Al, 6 Mo, 42 Ni, balance Fe) end at 1300.degree. F. Generally, rupture stress data for steel alloys are not given for temperatures in excess of 1700.degree.-1750.degree. F. Nimonic 115 (15% Cr, 4 Ti, 5 Al, 15 Co, 3.5 Mo, balance Ni; .rho.=499, a recent British turbine blade alloy) shows 12,000 psi rupture stress at 1832.degree. F. after only 100 hours.
Extrapolating from the available temperature ranges (a procedure not recommended in high-temperature fan design) for annealed 2.25 Cr-1 Mo steel to 1800.degree. F. one can obtain a Larson-Miller parameter P=45 and a rupture stress of 900 psi (nominal life to rupture 1 hour). Steel alloys used in reactor tubes such as the centrifugally cast 310 NK have been tested at 1900.degree. F. and P=56, exhibiting a 10.sup.4 hr rupture stress of 1250 psi. This rupture stress level for Incoloy is found at 1740.degree. F.
An estimate of stresses developed in high temperature fans may be obtained by considering a 1-ft long impeller blade on a 2-ft diameter hub to be a straight rod with a uniform cross-section. At 1000 rpm (209 ft/s tip speed), the stress at the root of the blade will be ##EQU5## in excess of the rupture stress of almost any high-alloy steel at temperatures 1800.degree. F. and higher. The maximum root stress may be reduced by tapering the profile, but the use of a safety factor (commonly 2 to 2.5) again puts it beyond a practical operating limit.
The situation up to the time of the invention has, therefore, been that unfortunately large quantities of heat energy have been locked in hot flue gases, unavailable to an energy-starved world.